The set of all values of `m` for which both the roots of the equation `x^2-(m+1)x+m+4=0` are real and negative is (a) `(-oo,-3]uu[5,oo)` (b) `[-3,5]` (c) `(-4,-3]` (d) `(-3,-1]`

Explanation

We have, `x^2+(m+1)x+m+4=0`

Discriminant is
`b^2-4ac`

=`(m+1)^2−4(m+4)=m^2−2m−15`
=`(m+3)(m−5)`

For roots to be real

Discriminant`>=0`

`m in (−oo,−3)uu[5,oo).....(1)`

Also for root to be negative
`alphabeta>0 and alpha+beta<0`

⇒`m+4>0 and −(m+1)<0`

...